All Questions
10
questions with no upvoted or accepted answers
5
votes
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answers
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Number of loops of a ball bouncing in a room with obstacles
Introduction
With a friend of mine we were studying the following problem: given a $m\times n$ grid draw this pattern (I don't know how to describe it in words)
The first image has $3$ loops and the ...
5
votes
0
answers
2k
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Good books to learn olympiad geometry,number theory, combinatorics and more
I want to start learning olympiad mathematics more seriously, and I would like to have advice on some good books or pdfs to learn with.
I have background but not a big background. For example I know ...
- 2,510
4
votes
0
answers
1k
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Counting the Number of Lattice Points in an $n$-Dimensional Sphere
Let $S_n(R)$ denote the number of lattice points in an $n$-dimensional "sphere" with radius $R$. For clarification, I am interested in lattice points found both strictly inside the sphere, and on its ...
- 1,022
1
vote
0
answers
33
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Different slopes defined by nesting $m$ polygons
I know that the vertices of a regular $n$-gon determines the total of $n$ different slopes. We nest the total of $m \in \mathbb{N}$ polygons by drawing a $(1/2)n$-gon inscribed inside the original ...
user830143
1
vote
0
answers
123
views
PDFs for Olympiad preparation
Could someone please recommend me some pdf files containing theory for topics that come up often in maths olympiads? I'm currently working through one about inequalities, and I'm really enjoying it. I ...
- 41
1
vote
0
answers
43
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In how many primitive pythagorean triples can some odd integer $a$ be a non-hypoteneuse edge?
In how many primitive pythagorean triples can some odd, positive integer $a$ be a non-hypoteneuse edge?
In the footnote to this question Daniel Fischer does most of the work:
Let $a$ be the odd ...
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1
vote
0
answers
420
views
Count points on x-axis
Given S and C . There are S sine functions and C cosine functions as following:
$F(i,x)$ = $sin(2^i x)$, $0 ≤ x ≤ 2π$, for $i = 0, 1, ..., S−1$
$G(j,x)$ = $cos(2^j x)$, $0 ≤ x ≤ 2π$, for $j = 0, 1,...
- 129
1
vote
0
answers
188
views
Number of classes of K-sets
I am having a plane in N dimension.
Th distance between 2 points (a1,a2,...,aN) and (b1,b2,...,bN) is max{|a1-b1|, |a2-b2|, ..., |aN-bN|}.
I need to to know how many K-sets exist(here K-set refers to ...
- 1,056
0
votes
0
answers
69
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Finding third side of non degenarate triangle
Given lengths of two sides of triangles $a$ and $b$, I want to calculate the number of possible integral values of length of third side $c$.
I know that range should be : $a-b<c<a+b$, given $a&...
- 113
0
votes
1
answer
171
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Counting points in/on cuboid
Given a cuboid that extend in x,y,z axis such that |x|≤N, |y|≤N, |z|≤N where N is given and can have value up to 10^9.Now a shooter is standing at origin (0,0,0).He need to shoot on any of the ...
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